In gear transmission designs, there is a growing demand for the apparently opposed requirements of carrying greater loads at higher speeds, with more reliability and quietness of operation. In part, these demands may be met to some extent by improved materials, better balancing, more nearly perfect machined surfaces, and more intensive attention to a myriad of design details. Such details include stringent mathematical analysis of both the kinematic and dynamic conditions of operation. An essential purpose of gear-tooth profiles is to transmit rotary motion from one shaft to another. In many cases, there is an additional requirement of uniform rotary motion. An almost infinite number of forms may be used as gear-tooth profiles. Although an involute profile is one of the most commonly used in conventional gear-tooth forms that are used to transmit power, occasions may arise when some other profile can be used to advantage. In all such mechanisms, even small deviations in rotational velocity can lead to poor machine performance, premature failure, and human discomfort caused by noise and vibrations in the working gears.
An ideal gear profile may be mathematically determined. Inevitably, surface deviations occur from the ideal profile. Such deviations tend to cause an excessive acceleration or deceleration of a driven gear in relation to a driving gear, which may in turn result in noise, vibration, and knocking. Such adverse effects may also be manifest in ideal gear profiles which are mounted with some degree of eccentricity. In general, kinematic error, or transmission error (TE), derives from instantaneous oscillations caused by production deviations of gear members from their proper theoretical parameters. Such errors arise from an actual positioning in space in relation to where a given point on the gear profile should be if no error existed. As a kinematic process, these errors produce acceleration and deceleration or torsional vibrations of the driven output shaft of a power transmission system. Another contributing factor may be the frequency with which meshing occurs between mating teeth. In some cases, such errors could be the source of dynamic torsional effects, which manifest themselves as kinematic errors.
One apparatus and method of measuring torsional vibration in a rotating shaft uses a laser doppler velocimeter (LDV) as described in U.S. Pat. No. 5,465,624, assigned to the assignee of the present application, which is incorporated herein in its entirety by reference. An LDV for use in such a system is available from the Bruel & Kjaer Company (Denmark) (Model 2523). This system allows an observer to measure torsional vibration of a rotating shaft by receiving a signal indicative of the deviation of instantaneous surface velocity from an average level.
A second LDV system was described in The Proceedings of the International Conference on Motion and Power Transmissions in Hiroshima, Japan on Nov. 23-26, 1991, which included a paper entitled "Measurement of Gear Transmission Error Using Laser Velocimeters", pages 225-229 ("Proceedings"). That paper discloses a gear transmission error measurement system using a laser to measure the surface speeds of objects. The system has two rotating gears having the same surface speeds. Because in "Proceedings" the surface speed is measured, shaft runouts and other eccentricities in the measurement device create errors in any measurements. Other measurement methods include Russian Reference No. 1966733, which discloses a seismic device that contacts the machine elements under observation and Russian Reference No. 698373, which discloses an optical encoder that measures kinematic errors in chains with non-integer ratios. These references are incorporated herein by reference. Other commercially available apparati for the determination of transmission errors (TE) in industrial mechanisms, such as reducers, gear boxes, and automotive axles, are available from suppliers including Ono-Sokki Company (Japan) and Gleason Works Company (U.S.A.).
The above methods and apparati measure kinematic error in rotating shafts, but the output of each may not be useful, as the magnitude of any transmission errors will be unknown until the measurement apparatus is calibrated. Known gear testers also have inherent measurement errors, which include errors input by the encoders. These errors are combined with the signal being measured. The combination of the error and the measured signal creates an output value. To separate these signals, it is necessary to determine the measurement error. This error presents a combination of systematic and stochastic components. Commercial test devices are often not directly calibrated by the manufacturer. In such instances, calibration is presumed from physical principles used in these testers. These presumptions rely upon the accuracy of key components produced by outside companies and on other unreliable methods. Where the instruments are not directly calibrated, the accuracy may be suspect, so the user of such devices may conduct various procedures and tests to confirm the accuracy of the apparatus. If the manufacturer directly calibrates the apparatus, typically such calibration is performed by the manufacturer prior to shipment of the device. An example of such calibration may include adding physical sensors to the apparatus to measure errors. These techniques are done at the manufacturer, where the apparatus is produced. However, these techniques provide additional errors and therefore each subsequent measurement with the apparatus includes the prior error. Furthermore, the apparatus is not easily verified at the customer's site, and any error that occurs after the apparatus leaves the manufacturer is incorporated into any subsequent measurements.
In IMECHE 1991, pages 431-436, J. D. Smith describes in "Practical Rotary Encode Accuracy Limits for Transmission Error Measurement" the error in calibration from the manufacturer and further describes the difficulty of obtaining an accurate calibration. In this article, a calculation is provided for a repetitive test which is subject to inherent residual errors in the machine.
It would be desirable to provide a method of testing a device for checking the accuracy of power transmission mechanisms, particularly a method which may be easily used to calibrate such devices in a production environment.